d2_absolute_error_score

sklearn.metrics.d2_absolute_error_score(y_true, y_pred, *, sample_weight=None, multioutput='uniform_average')

\(D^2\) regression score function, fraction of absolute error explained.

Best possible score is 1.0 and it can be negative (because the model can be arbitrarily worse). A model that always uses the empirical median of y_true as constant prediction, disregarding the input features, gets a \(D^2\) score of 0.0.

Read more in the User Guide.

Added in version 1.1.

Parameters:

y_truearray-like of shape (n_samples,) or (n_samples, n_outputs)

Ground truth (correct) target values.

y_predarray-like of shape (n_samples,) or (n_samples, n_outputs)

Estimated target values.

sample_weightarray-like of shape (n_samples,), default=None

Sample weights.

multioutput{‘raw_values’, ‘uniform_average’} or array-like of shape (n_outputs,), default=’uniform_average’

Defines aggregating of multiple output values. Array-like value defines weights used to average scores.

‘raw_values’ :

Returns a full set of errors in case of multioutput input.

‘uniform_average’ :

Scores of all outputs are averaged with uniform weight.

Returns:

scorefloat or ndarray of floats

The \(D^2\) score with an absolute error deviance or ndarray of scores if ‘multioutput’ is ‘raw_values’.

Notes

Like \(R^2\), \(D^2\) score may be negative (it need not actually be the square of a quantity D).

This metric is not well-defined for single samples and will return a NaN value if n_samples is less than two.

References

[1]

Eq. (3.11) of Hastie, Trevor J., Robert Tibshirani and Martin J. Wainwright. “Statistical Learning with Sparsity: The Lasso and Generalizations.” (2015). https://hastie.su.domains/StatLearnSparsity/

Examples

>>> from sklearn.metrics import d2_absolute_error_score
>>> y_true = [3, -0.5, 2, 7]
>>> y_pred = [2.5, 0.0, 2, 8]
>>> d2_absolute_error_score(y_true, y_pred)
0.764...
>>> y_true = [[0.5, 1], [-1, 1], [7, -6]]
>>> y_pred = [[0, 2], [-1, 2], [8, -5]]
>>> d2_absolute_error_score(y_true, y_pred, multioutput='uniform_average')
0.691...
>>> d2_absolute_error_score(y_true, y_pred, multioutput='raw_values')
array([0.8125    , 0.57142857])
>>> y_true = [1, 2, 3]
>>> y_pred = [1, 2, 3]
>>> d2_absolute_error_score(y_true, y_pred)
1.0
>>> y_true = [1, 2, 3]
>>> y_pred = [2, 2, 2]
>>> d2_absolute_error_score(y_true, y_pred)
0.0
>>> y_true = [1, 2, 3]
>>> y_pred = [3, 2, 1]
>>> d2_absolute_error_score(y_true, y_pred)
-1.0